SNVA994 Application note

SNVA994A February 2022 – March 2023 LM5157 , LM5157-Q1 , LM51571-Q1 , LM5158 , LM5158-Q1 , LM51581 , LM51581-Q1

3.3 Slope Compensation Check

According to the theory of the peak current mode control, the slope of the compensation ramp must be greater than half of the sensed inductor current falling slope to prevent subharmonic oscillation at high duty cycle. Therefore, the following inequality in Equation 9 should be satisfied.

Equation 9.

0.5 \times \frac{(V_{LOAD} + V_{F}) - V_{SUPPLY}}{L_{M}} \times A_{CS} \times Margin < 500 mV \times f_{sw}

where

A_CS is the equivalent current sensing gain.
500mV is the slope compensation peak voltage.

Typically 82% of the sensed inductor current falling slope is an optimal value of the slope compensation, which reflects to a margin of 1.6. If the inequality is failed, the inductance value of L_M must be increased so that the falling slope can be smaller. If the L_M inductance value is changed the peak current must be re-calculated and the device selection must be re-examined. In this example, the inequality is verified in Equation 10, Equation 11, and Equation 12.

Equation 10.

0.5 \times \frac{(V_{LOAD} + V_{F}) - V_{SUPPLY}}{L_{M}} \times A_{CS} \times Margin = 0.5 \times \frac{(10 V + 0.5 V) - 8 V}{8 μH} \times 0.095 \times 1.6 = 23. 75 \times 10^{3}

Equation 11.

500 mV \times f_{sw} = 500 mV \times 250 k Hz = 125 \times 10^{3}

Equation 12.

23. 75 \times 10^{3} < 125 \times 10^{3}